No. You will not be able to access the Beat Board or Outline Editor features from Final Draft Writer.
If you would like to use these features, you will need to open your file in the desktop version of Final Draft 13.
For further information on utilizing the Beat Board and Outline Editor you can visit these links:
How do I use the Outline Editor?
If you need to install your copy of Final Draft 13, you can do so here:
https://www.finaldraft.com/support/manuals-and-software/fd13/